Question

If $a=2\sqrt{2},b=6,A={45}^0,$then

• A. no triangle is possible
• B. one triangle is possible
• C. two triangle are possible
• D. either no triangle or two triangles are possible

Answer 1

The correct option is A

no triangle is possible

$\text{Using sine rule,}\frac{a}{sinA}=\frac{b}{sinB}\Rightarrow \frac{2\sqrt{2}}{sin{45}^0}=\frac{6}{sinB}\Rightarrow sinB=\frac{6}{2\sqrt{2}}\times \frac{1}{\sqrt{2}}=\frac{6}{4}=\frac{3}{2}>1$

Which is not possible.

Hence no triangle is possible